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Dynamics at Fluid Solid Interfaces: Porous Media and Colloidal Particles

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Principles of Soft-Matter Dynamics

Abstract

This chapter could be entitled “molecular motions in complex media” as well. The point is that the systems of interest can be defined by the existence of fluid–solid interfaces. Surface-related phenomena are therefore of central interest. There is an endless list of examples belonging to this category in principle. Emphasis will be laid on porous glasses, fine-particle agglomerates, biopolymer solutions, lipid bilayers, biological tissue, etc. The predominant purpose of this chapter is to elaborate a well-classified scheme of the key mechanisms determining molecular dynamics in the presence of fluid–solid interfaces. This includes adsorption and exchange kinetics, translational and rotational diffusion, and liquid/vapor coexistence phenomena. Effects due to fluid–wall interactions on the one hand and, on the other hand, owing to geometric confinement in mesoscopic pore spaces will thoroughly be discriminated.

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Notes

  1. 1.

    A first application of this process was already mentioned at the end of Sect. 6.8.4 as a mechanism competing with shape fluctuations of lipid vesicles.

  2. 2.

    A short side note: “Exchange” is to refer to molecular exchange if not specified otherwise. Selective exchange of atoms such as hydrogen in water or in hydroxyl groups of other compounds, for example, is usually slower and therefore irrelevant in the present context. For example, hydrogen exchange in water of neutral acidity has an exchange time from molecule to molecule in the order of 10−3 s [20, 21] compared to exchange times of about 10−5 s for molecular exchange between adsorbed and bulk-like water phases. The latter order of magnitude is concluded from the strong frequency dependence of the spin–lattice relaxation time in such systems ranging down to the kHz regime (see Fig. 7.3).

  3. 3.

    Anomalies are however expected on shorter time scales below the ms regime as they are accessible with the fringe-field variant of field-gradient diffusometry. In this case, anomalies have been observed indeed (see Ref. [29]).

  4. 4.

    Trade names of frequently studied, more or less monodisperse silica fine particles are Alfasil and Cab-o-sil with diameters ranging from a few up to several tens of nanometers.

  5. 5.

    Under such conditions, one must make sure that all remaining pore space is actually filled with liquid. Otherwise, a third phase, namely, the vapor of the liquid, can contribute or even dominate. This phenomenon will be discussed in Sect. 7.4.4.

  6. 6.

    Immaterial diffusion of spins by flip-flop spin transitions in the frozen material, the so-called spin diffusion mentioned several times before, can be excluded for deuterons but might be effective for protons in principle. By all means, the influence on the diffusion behavior in the liquid phase will be entirely negligible, owing to the weak coupling between fluid and solid [23, 40].

  7. 7.

    Incidentally, the peculiar thermodynamic properties of interfacial water at low temperatures have found much attention especially in the biopolymer community. The ongoing discussion of this topic is demonstrated by a recent quasi-elastic neutron scattering study reported in Ref. [41] and other references cited therein.

  8. 8.

    Note that – irrespective of the nonfreezing surface layers – the freezing temperature of the bulk-like phase is reduced slightly according to the Gibbs/Thomson relation which predicts a depression proportional to the surface-to-volume ratio of the pores [46]. On this basis, NMR techniques have been suggested for the determination of the pore size and its distribution [47, 48]. With these methods, the freezing temperature is determined by the more or less abrupt change of the NMR linewidth at the phase transition.

  9. 9.

    It should be emphasized that this approach is appropriate for translational diffusion at typical experimental time and length scales. A totally different situation arises for rotational diffusion as probed by spin relaxation to be discussed further down.

  10. 10.

    A detailed analysis of echo formation mechanisms can be found in Ref. [39].

  11. 11.

    Provided that motional averaging is still incomplete, the preferential orientation of adsorbate molecules relative to adsorbent surfaces can be demonstrated by dipolar or quadrupolar splitting of NMR resonance lines [74, 75] or, if such splitting is not resolved, by multiple-quantum filtering spectroscopy which is based on residual dipolar or quadrupolar couplings [76, 77].

  12. 12.

    An analogous (one-dimensional) analysis has been employed above for polymer conformations as illustrated in Fig. 5.22.

  13. 13.

    An analogous strategy has been pursued in the experiments represented by Fig. 5.41 in the context of the corset effect of polymers under mesoscopic confinement.

  14. 14.

    The residual correlation of local motions must not be identified with the residual dipolar or quadrupolar coupling as revealed in NMR spectroscopy [74–77]. The time scales can be very different. By tendency, these phenomena are however related with each other. The common basis is the anisotropy of local reorientations.

  15. 15.

    Recall the analogous scenarios treated in the context of polymers (Eq. 5.295) and liquid crystals (Eq. 6.104). The analytical form of a product is a consequence of probability theory. The product implies the joint probability that none of the three independent reorientation processes have yet become effective. In other terms, it is the probability that the orientation correlation is still retained at time \( t \).

  16. 16.

    With the surface diffusion coefficient discussed below, this correlation time limit means root-mean square-surface displacements much less than a few Å. Compare Sect. 7.4.2.1, where translational diffusion in the adsorbed phase has been examined.

  17. 17.

    The analytical structure of Eq. (7.102) can be rationalized as follows: The correlation function effective in the crossover regime is composed of the statistically independent partial correlation functions for tumbling on the one hand and for the longest RMTD mode on the other. That is exp \( \left\{ { - {{t} \left/ {{{{\tau}_{{\rm c}}}}} \right.}} \right\} = \exp \left\{ { - {{t} \left/ {{{{\tau}_{{{\rm tumble}}}}}} \right.}} \right\}\exp \left\{ { - {{t} \left/ {{{{\tau}_{{\rm l}}}}} \right.}} \right\} \) with \( {{\tau}_{{\rm c}}} = {{\left( {\tau_{{\rm tumble}}^{{ - 1}} + \tau_{{\rm l}}^{{ - 1}}} \right)}^{{ - 1}}} \).

  18. 18.

    Note that this value must simultaneously be taken as the upper limit of the exchange time between the adsorbed and bulk-like phases. That is, \( {{\tau}_{{{\rm l}}}} < {{\tau}_{{\rm ex}}} \) as anticipated for slow exchange on the correlation time scale.

  19. 19.

    In Ref. [95], some modification of this law is suggested based on a pulsed photoexcitation study of labeled proteins. For the present treatment, this is however of little relevance.

  20. 20.

    For an explanation of this sort of powder spectrum, see Ref. [39], for instance.

  21. 21.

    A complete expression for the BMSD propagator on planar surfaces has recently been derived in Ref. [19]. This implies the prevalence of a Cauchy distribution at short displacements (as they are relevant in the present case) and a terminating Gaussian decay in the limit of long distances.

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    Rainer Kimmich

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Kimmich, R. (2012). Dynamics at Fluid Solid Interfaces: Porous Media and Colloidal Particles. In: Principles of Soft-Matter Dynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5536-9_7

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